Noether’s Theorem

Abstract

A major contribution to the development of the physics of fundamental interactions, in fact for the whole physics, was the theorem developed by Emmy Noether in 1918 [10, 105, 106], showing how to construct the observables of a theory, given its Lagrangian and Lie symmetry groups. Following Lopes, for pedagogical purposes we divide the theorem in three parts, one for each kind of symmetry considered: transformation of coordinates in space–time, global gauge transformations, and local gauge transformations [107]. We also include separately the specific case of general relativity with its peculiar diffeomorphism invariance.